It is easy to see the spread of data from a box and whisker plot because it is all shown on the one diagram. It is also good for comparing different sets of data.
Cumulative frequency diagram:
Cumulative frequency is the total of all the frequencies of a set of data up to any piece or group of data. A cumulative frequency diagram is a diagram of which all different cumulative frequencies are plotted.
Pie chart:
A pie chart is a circular frequency diagram which uses sectors. A pie chart is drawn using angles and percentages. 360º represents 100%. For each gender and year group I will work out what percentage of people have the same hand span. I will round the figures up or down as appropriate. I will then use the percentages to work out the degrees. This is an easy to understand diagram and is also good for comparing different sets of data.
Frequency Polygon:
A frequency polygon uses bars to display grouped data on a continuous scale. To draw a frequency polygon I will need to draw an axis with ‘hand span (cm)’ along the x axis and frequency going up the y axis. I will then plot a bar chart but I will draw it without gaps. I will then take the mid point of each bar and join them up with straight lines to make a frequency polygon.
A table showing male hand span measurements between years 7-11.
In this data there are two obvious outliers they are highlighted in yellow.
A table showing female hand span measurements between years 7-11.
In this data there is one obvious outlier it is highlighted in yellow.
The data value highlighted in red could also be an outlier; however it is not quite as obvious. This outlier could have occurred by either a typing mistake or by the pupil not knowing the correct way to measure it. However it is possible to have a 9 cm hand span but it is just unlikely. As a result of these outliers I will substitute them with the next closest value. I will not do this for the 9 cm hand span. I will do this for the values highlighted in yellow because they will have a dramatic affect on the averages by making them a lot higher. By substituting the averages it will make them a lot more accurate and we will have a better idea of the average pupil’s hand span measurement.
These tables show the hand span measurements for year 7 to 11. They were picked systematically; by choosing every fifth male and every fifth female in regular intervals. If there weren’t enough people to choose every fifth person I would go through the data again, missing out the people who had already been highlighted but still choosing every fifth person until I had a sample of 30 for each gender in each year from years 7 to 11.
The averages and the range:
Male:
Female:
These were the averages from my original data sample. I changed the outliers to give more accurate results and they are shown in the table below.
Male:
Female:
The highlighted columns are the averages that have been changed. I changed the numbers 50.2 and 64 with the numbers 17.5 and 18.8 as they were the next numbers after the outliers. I changed these two numbers in the highlighted column (year 8) for the males. In the female table I changed the number 45 with16 for the highlighted column (year 7).
These tables show that my hypothesis is partly right because the averages are bigger for boys hand spans than they are for girls in each year group apart from year 7 which is by a very small amount.. These tables also show that the female’s data varies more in the first three years as the range is bigger, they then begin to become more grouped as you start to look at the two older years.
Pie charts
I rounded the decimal numbers up or down to the closest whole number and then drew them on the circle. 360º represents the whole of the data (100%) and if there was only one person who had a particular hand span measurement then the degree would be 12 because 360/30=12. To work out the degree I needed for each size I had to find out how many people had that measurement in the year I was doing, divide it by thirty because that is how big the sample is and then times by 360 and that would tell me the number of degrees needed to represent the number on the circle. For example if there were twelve people in year seven with a hand span measurement of 20, I would then work out the degree by doing this calculation:
12/30=0.4
0.4*360=144
I would then draw a line on the graph and then draw a line from that, that measures144º. After that I would then work out the next hand span measurement and draw the degree on the graph.
The degrees I worked out and drew on the pie charts are drawn in these tables:
Male year 7
Female year 7
Male year 8
Female year 8
Male year 9
Female year 9
Male year 10
Female year 10
Male year 11
Female year 11
These tables show how many people had a particular hand span measurement and the numbers that I rounded up are included in the table. The table also shows the number of degrees I drew on the circle to make the pie charts for each year group which are on the next page.
Analysis-pie charts.
The pie charts that I have drawn tell us what the most occurring number is in the set of data for that age group and it is easy to compare the different years with each other as I have used the same key. The bigger the segment means the more people who had that sized hand span. The pie charts show us the mode but in a diagram that is easy to read.
The measurements that the most people had and the least people had are:
Year 7 male
Most- 18, 19 and 20cm which 7 people had one of those measurements this meant that a 84 º angle was drawn on the circle to represent each measurement.
Least- 13 and 15 which only 1 person had, this meant that a 12º angle was drawn on the circle to represent each measurement.
Year 7 female
Most-18 and 19cm which 8 people had one of those measurements this meant that a 96º angle was drawn on the circle to represent each measurement.
Least- 20, 22 and 25cm which only one person had each of those measurements so a 12 º angle was drawn.
Year 8 male
Most- 19 and 21cm which 9 people had each of those measurements, this meant a 108 º angle was drawn on the circle for each of these measurements.
Least- 16 and 22cm which only 1 person had each of these measurements, this meant a 12 º angle was drawn.
Year 8 female
Most- 18 which 11cm people had, this meant a 132 º angle was drawn.
Least- 14 and 15cm which only 1 person had each of these measurements. A 12º angle was drawn on the circle.
Year 9 male
Most- 22 which 8cm people had so a 96 º angle was drawn.
Least- 12, 16 and 17cm which 1 person had each of these measurements. A 12 º angle was drawn for these measurements on the pie chart to represent the year 9 males.
Year 9 female
Most- 19 which 11cm people had so a 132 º angle was drawn.
Least- 9 and 23cm in which only 1 person had each measurement. A 12 º angle was drawn.
Year 10 male
Most- 22 and 24cm which 6 people had so a 72 ºangle was drawn.
Least- 18cm which only one person had. So a 12 º angle was drawn.
Year 10 female
Most- 20cm which 14 people had so a 168 º angle was drawn.
Least- 15, 21 and 22cm which one person had each measurement, so this meant a 12 º angle was drawn for each measurement.
Year 11 male
Most- 22cm which 10 people had so a 120 º angle was drawn.
Least- 15, 17 and 18cm which one person had each of, so a 12 º angle was drawn.
Year 11 female
Most- 19 which 8cm people had so a 96 º angle was drawn.
Least- 16 and 22cm which only one person had so a 12 º angle was drawn.
Cumulative frequency tables for hand span data of year 7 to 11 males and females.
Year 7
Male
Female
Year 8
Male
Female
Year 9
Male
Female
Year 10
Male
Female
Year 11
Male
Female
These tables show the frequency and cumulative frequency for each year group. The cumulative frequency is the frequency added up as it goes along. With these graphs, I did not expect to see the actual quartiles and median because the data involved decimals which meant they had to either be rounded up or down. As a result the quartiles have slightly changed because of this.
Analysis- Cumulative frequency and Box Plots
From the graphs I have drawn I have made the following observations:
- Year 7 females have a higher range of data than year 7 males.
- Year 7 females have a larger and higher inter-quartile range than year 7 males.
- Year 7 males have a higher median than year 7 females.
- The lowest and highest value for year 7 females is higher than the males.
Therefore this shows that females have higher quartiles for this age group than males. The following results show the quartiles and median when read off the graph:
- Year 8 females have a higher range of data than the males.
- The year 8 males have a higher inter-quartile range and median than the year 8 females.
- Year 8 males have a more spread out range.
The box plots show that year 8 boys have bigger hand spans than year 8 girls. This is because the interquartile range is higher however the females have a higher lowest value. This could mean that no female in year 8 out of the people selected had a small hand span. The following results show the quartiles and median when read off the graph:
- Year 9 females have a higher range of data than the males.
- The year 9 males have a higher inter-quartile range and median than the year 9 females.
- Year 9 males have a more spread out range.
This again shows that boys have bigger hand spans than girls at this age group, because they have higher quartiles and the only point lower is the lowest value which could have been a small outlier as it is about 3 or 4cm away from the next male up.
The following results show the quartiles and median when read off the graph:
- Year 10 males and females
- All points on the graphs show that males have higher quartiles and medians than females.
This shows once again that boys in this age group generally have bigger hand spans than girls because all points that the graphs show are bigger for males. The lowest value, the highest value, the lower quartile, the median, the inter quartile range and the upper quartile are all bigger for males than they are for the females. The following results show the quartiles and median when read off the graph:
- Year 11 males and females
- All points on the graphs show that males have higher quartiles and medians than females.
This again shows that males have bigger hand spans than females at this age group. The following results show the quartiles and median when read off the graph:
These box plots back up my hypothesis because they show that males have bigger hand spans overall in the last 4 years the only age group that doesn’t back it up is year 7. This might be because girls are generally almost fully grown by year 7/8 which means that they don’t grow as much during the final years.
Conclusion:
From the graphs and averages that I have worked out I can clearly tell that boys generally do have bigger hand spans than girls which proves that my hypothesis is correct.
